Define the series
Tn=k=1∑n(3k+1)(21)k−1.
(i) Rewrite Tn as a combination of two separate summations, each of which can be evaluated using a standard formula.
(ii) Hence obtain a simplified closed-form expression for Tn in terms of n.
(iii) Using your result from part (ii), calculate T10 correct to two decimal places.